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Assessment of Complex System Dynamics via Harmonic Mapping in a Multifractal Paradigm

Author

Listed:
  • Gabriel Gavriluț

    (Faculty of Phisics, Alexandru Ioan Cuza University, Bulevardul Carol I nr. 11, 700506 Iași, Romania)

  • Liliana Topliceanu

    (Faculty of Engineering, Vasile Alecsandri University of Bacau, 600115 Bacau, Romania)

  • Manuela Gîrțu

    (Department of Mathematics and Informatics, Vasile Alecsandri University of Bacau, 600115 Bacau, Romania)

  • Ana Maria Rotundu

    (Faculty of Phisics, Alexandru Ioan Cuza University, Bulevardul Carol I nr. 11, 700506 Iași, Romania)

  • Stefan Andrei Irimiciuc

    (National Institute for Laser, Plasma and Radiation Physics, 409 Atomistilor Street, 077125 Bucharest, Romania
    Romanian Scientists Academy, 54 Splaiul Independentei, 050094 Bucharest, Romania)

  • Maricel Agop

    (Romanian Scientists Academy, 54 Splaiul Independentei, 050094 Bucharest, Romania
    Department of Physics, “Gh. Asachi” Technical University of Iasi, 700050 Iasi, Romania)

Abstract

In the present paper, nonlinear behaviors of complex system dynamics from a multifractal perspective of motion are analyzed. In the framework of scale relativity theory, by analyzing the dynamics of complex system entities based on continuous but non-differentiable curves (multifractal curves), both the Schrödinger and Madelung scenarios on the holographic implementations of dynamics are functional and complementary. In the Madelung scenario, the holographic implementation of dynamics (i.e., free of any external or internal constraints) has some important consequences explicated by means of various operational procedures. The selected procedures involve synchronous modes through SL (2R) transformation group based on a hidden symmetry, coherence domains through Riemann manifold embedded with a Poincaré metric based on a parallel transport of direction (in a Levi Civita sense). Other procedures used here relate to the stationary-non-stationary dynamics transition through harmonic mapping from the usual space to the hyperbolic one manifested as cellular and channel type self-structuring. Finally, the Madelung scenario on the holographic implementations of dynamics are discussed with respect to laser-produced plasma dynamics.

Suggested Citation

  • Gabriel Gavriluț & Liliana Topliceanu & Manuela Gîrțu & Ana Maria Rotundu & Stefan Andrei Irimiciuc & Maricel Agop, 2021. "Assessment of Complex System Dynamics via Harmonic Mapping in a Multifractal Paradigm," Mathematics, MDPI, vol. 9(24), pages 1-15, December.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:24:p:3298-:d:705498
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    Cited by:

    1. Maria Luminita Scutaru & Catalin-Iulian Pruncu, 2022. "Mathematical Modeling and Simulation in Mechanics and Dynamic Systems," Mathematics, MDPI, vol. 10(3), pages 1-6, January.

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